A 3 m long, horizontal, rigid, uniform beam PQ has negligible mass. The beam is subjected to a 3 kN concentrated vertically downward force at 1 m from P, as shown in the figure. The beam is resting on vertical linear springs at the ends P and Q. For the spring at the end P, the spring constant $K_P$ = 100 kN/m.

If the beam DOES NOT rotate under the application of the force and displaces only vertically, the value of the spring constant $K_Q$ (in kN/m) for the spring at the end Q is

A horizontal force of P kN is applied to a homogeneous body of weight 25 kN, as shown in the figure. The coefficient of friction between the body and the floor is 0.3. Which of the following statements is/are correct?

Under the action of a concentrated load P at C as shown, the magnitude of tension developed in the rope is

The beam shown in the figure is subjected to a uniformly distributed downward load of intensity $q$ between supports A and B.

Considering the upward reactions as positive, the support reactions are

A uniform rod KJ of weight w shown in the figure rests against a frictionless vertical wall at the point K and a rough horizontal surface at point J. It is given that w = 10 kN, a = 4 m and b = 3 m.

The minimum coefficient of static friction that is required at the point J to hold the rod in equilibrium is __________. (round off to three decimal places)